I think I learnt to explain this more clearly this week...
On one hand, Paul clearly sees the obligation to obey the Law as having been abolished in Jesus (e.g Galatians 4:21-31). On the other hand, he clearly sees the Law as undergirding a lot of his arguments and his ideas about what is moral.
I think Colin Kruse summarises the situation well.
The Mosaic law was not their law, any more than the Mosaic covenant was their covenant. However, the OT in its entirety, including the law, was their Scripture, and that meant that it was useful for ‘teaching, rebuking, correcting and training in righteousness’ (2 Tim. 3:16 NIV), as long as it was read paradigmatically and not applied literally.
New Dictionary of Biblical Theology
So the Law in the Old Testament isn't our Law, but it is still our Scripture. It can still tell us what sin is, for example, and what God is like and what people are like, but it isn't a Law that we have to obey. Paul's description of what Christians are to do to the Law isn't obedience - it's fulfilment.
1 Corinthians 10 is a great example of this. Paul can say all of the following things to a group of (largely) Gentiles:
- The ancient Israelites are "our forefathers" v1
- They drank from Christ v4
- They are (counter-)examples for us v6, 11
- The Bible was written for the Church v11
- The fulfilment of the ages has come upon us v11.
We are not under the Law. But the Law is still our Scripture, and it still tells us what sin is, and we should not sin. It still tells us what God is like, and we should not disregard that.